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Quark matter meets cold atoms
474th International Wilhelm und Else Heraeus Seminar on
Strong interactions: from methods to structures, Bad Honnef, Feb 12-16, 2011
Mei Huang IHEP, CAS
TPCSF, CAS
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Content
I. Recent progress of QCD phase structure
Cold quark matter & cold atoms
II. Interplay between chiral and
deconfinement phase transitions
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I. Recent Progress of QCD phase structure
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QCD phase diagram: 1974 ---- 1999
For physical quark mass, crossover at zero and small baryon density, and first order phase transition at finite baryon density. CEP is the end point of first order phase transition.
HM
QGP
CEP
Heating QCD vacuum: (RHIC, LHC, early universe)
1, Chiral symmetry restoration
2, Deconfinement phase transition
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QCD phase diagram after 1999
Squeezing QCD matter: Color superconductor
HM
QGP
CSC
Pairing with mismatch beta-equilibrium,
charge neutrality
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Imbalanced CSC meets imbalanced cold atoms
MH, I.Shovkovy, PRD70:051501,2004; 094030,2004
Shovkovy, M.H, PLB564:205,2003M.H., I. Shovkovy, NPA729:835,2003
Interior gap & Breached Pairing
Liu,Wilczek, PRL90:047002,2003Gubankova, Liu, Wilczek, PRL91:032001,2003
Gapless 2SC phase
Chromomagnetic instability Superfluid density is negative
Wu, Yip, PRA67: 053603, 2003
Other possibilities: LOFF state(1964), phase separation
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Zwierlein, Schirotzek, Schunck, & Ketterle, Science 2005, cond-mat/0511197Partridge, Li, Kamar, Liao, & Hulet, Science 2005, cond-mat/0511752.
n1=n2
n1>>n2
phase separation
Imbalanced pairing in cold atom system
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M.H. PRD73:045007, 2006; Int.J.Mod.Phys.A21, 910, (2006)
I. Giannakis, D.F.Hou, M.H., H.C.Ren, PRD75:011501,2007, PRD75:014015,2007
Group G
Subspace: Group H
Coset space: M=G/H
Instability of NG bosons FF-like stateHiggs instability spatial inhomogeneity
For gapless superfluidity (BP) state, no charge Coulomb energycompetes with Higgs instability, phase separation is more favored.
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9Abuki-Baym-Hatsuda-Yamamoto, arXiv:1003.0408
BCS-BEC crossover
Abuki,
He, Zhuang,
Deng, Pu, Wang
Abuki-Baym-Hatsuda-Yamamoto ……
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10Compact Star
sQGP
QCD phase diagram High T part after 2003
P. Romatschke, U. Romatschke, Phys.Rev.Lett.99:172301,2007
Discovery of sQGP at RHIC
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Viscosity/entropy density (units of ) Bk/
He near point
QGP simulations
String theory limit
Slide from John E. Thomas
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II. Interplay between chiral and deconfinement phase transitions
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2007: Quarkyonic phase chiral symmetric but confined phase
L. McLerran, R. Pisarski 2007
Phase diagram at large Nc Conditions:• Large Nc• Deconfined quark Fermi surface
Particle-particle pairing is suppressed
Particle-hole (color singlet) pairing dominant
chiral density wave
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Can “Quarkyonic phase” be realized in real QCD?
Fukushima, Hatsuda, arXiv:1005.4814
“Quarkyonic phase” has extended meaning, here indicates chiral symmetric but confined phase.
More interests are attracted to the relation between
chiral and deconfinement phase transitions
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Lattice results on chiral and deconfinement phase transitions at zero mu
Chiral limit: coincide
Physical quark mass (2+1):
RBC-Bielefeld: coincide
Wuppertal-Budapest: (crossover feature)
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Relation between chiral and deconfinement phase transitions in PNJL or PLSM model
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Order parameter of center symmetry: Polyakov loop
Confinement: center symmetry
Deconfinement:
center symmetry breaking
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Relation between chiral and deconfinement phase transitions in PNJL model
Different choices of Polyakov potential: fixed by lattice QCD at finite T
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Sasaki,Friman,Redlich, hep-ph/0611147
Kenji Fukushima, arXiv:0803.3318
Chiral symmetry broken and deconfined / coincidence
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Chiral symmetric but confined phase in PLSM model
H. Mao, J. Jin, MH, arXiv:0906.1324, J.Phys.G37:035001,2010
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In PNJL or PLSM model, at zero baryon density, whether chiral phase transition and deconfinement phase transition coincide or not depends much on parameters used.
In these models, there are no real interplay between chiral phase transition and deconfinement phase transition.
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Dressed Polyakov loop
An equivalent order parameter for deconfinement phase transition:
Gattringer,PRL97(2006)032003Bilgici et.al. PRD77(2008)094007Braun, Hass,Marhauser,Pawlowski, arXiv:0908.0008
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Order parameter of center symmetry:
Dressed Polyakov loop or dual chiral condensateGattringer,PRL97(2006)032003
n=1: dressed Polyakov loop
Dressed Polyakov on lattice: Bilgici et.al. in DSE: Fischer et.al.
Linking confinement to spectral properties of Dirac operator
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The periodicity property of the quark fields change under the the gauge transformation Uz:
Dual observables:
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Dressed Polyakov loop in NJL model
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Chiral limit: coincide
T.Mukherjee, H.Chen, M.Huang, arXiv:1005.2482,PRD82:034015,2010
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Physical quark mass:
crossover region
T.Mukherjee, H.Chen, M.Huang, arXiv:1005.2482,PRD82:034015,2010
Y.Aoki, Z.Fofor,A.Katz,K.Szabo,hep-lat/0609068, PLB643:46-54,2006
1st order:
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Why for 1st phase transition?
T.Mukherjee, H.Chen, M.Huang, arXiv:1005.2482,PRD82:034015,2010
for 1st phase transitionis preserved by the singularity.
If this is true, there will be no “quarkyonic” phase or chiral symmetric but confined phaseat finite density.
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Nf=2+1 NJL model: sequential (flavor dependent) phase transitions
Fukun Xu, T.Mukherjee, M.H., arXiv:1101.2952
CEP related to future RHIC and FAIR Exp. will be the CEP of light u,d quarks
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Summary
1, Much progress on QCD phase diagram at finite temperature and density has been made in the last 10 years.
2, Quantitative results are still few!